3 /* Subroutine */ int slasq4_(integer *i0, integer *n0, real *z__, integer *pp,
4 integer *n0in, real *dmin__, real *dmin1, real *dmin2, real *dn,
5 real *dn1, real *dn2, real *tau, integer *ttype)
11 /* System generated locals */
15 /* Builtin functions */
16 double sqrt(doublereal);
24 /* -- LAPACK auxiliary routine (version 3.1) -- */
25 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
28 /* .. Scalar Arguments .. */
30 /* .. Array Arguments .. */
36 /* SLASQ4 computes an approximation TAU to the smallest eigenvalue */
37 /* using values of d from the previous transform. */
39 /* I0 (input) INTEGER */
42 /* N0 (input) INTEGER */
45 /* Z (input) REAL array, dimension ( 4*N ) */
46 /* Z holds the qd array. */
48 /* PP (input) INTEGER */
49 /* PP=0 for ping, PP=1 for pong. */
51 /* N0IN (input) INTEGER */
52 /* The value of N0 at start of EIGTEST. */
54 /* DMIN (input) REAL */
55 /* Minimum value of d. */
57 /* DMIN1 (input) REAL */
58 /* Minimum value of d, excluding D( N0 ). */
60 /* DMIN2 (input) REAL */
61 /* Minimum value of d, excluding D( N0 ) and D( N0-1 ). */
66 /* DN1 (input) REAL */
69 /* DN2 (input) REAL */
72 /* TAU (output) REAL */
73 /* This is the shift. */
75 /* TTYPE (output) INTEGER */
82 /* ===================================================================== */
84 /* .. Parameters .. */
86 /* .. Local Scalars .. */
88 /* .. Intrinsic Functions .. */
90 /* .. Save statement .. */
92 /* .. Data statement .. */
93 /* Parameter adjustments */
98 /* .. Executable Statements .. */
100 /* A negative DMIN forces the shift to take that absolute value */
101 /* TTYPE records the type of shift. */
103 if (*dmin__ <= 0.f) {
109 nn = (*n0 << 2) + *pp;
112 /* No eigenvalues deflated. */
114 if (*dmin__ == *dn || *dmin__ == *dn1) {
116 b1 = sqrt(z__[nn - 3]) * sqrt(z__[nn - 5]);
117 b2 = sqrt(z__[nn - 7]) * sqrt(z__[nn - 9]);
118 a2 = z__[nn - 7] + z__[nn - 5];
122 if (*dmin__ == *dn && *dmin1 == *dn1) {
123 gap2 = *dmin2 - a2 - *dmin2 * .25f;
124 if (gap2 > 0.f && gap2 > b2) {
125 gap1 = a2 - *dn - b2 / gap2 * b2;
127 gap1 = a2 - *dn - (b1 + b2);
129 if (gap1 > 0.f && gap1 > b1) {
131 r__1 = *dn - b1 / gap1 * b1, r__2 = *dmin__ * .5f;
141 r__1 = s, r__2 = a2 - (b1 + b2);
145 r__1 = s, r__2 = *dmin__ * .333f;
155 if (*dmin__ == *dn) {
158 if (z__[nn - 5] > z__[nn - 7]) {
161 b2 = z__[nn - 5] / z__[nn - 7];
164 np = nn - (*pp << 1);
167 if (z__[np - 4] > z__[np - 2]) {
170 a2 = z__[np - 4] / z__[np - 2];
171 if (z__[nn - 9] > z__[nn - 11]) {
174 b2 = z__[nn - 9] / z__[nn - 11];
178 /* Approximate contribution to norm squared from I < NN-1. */
181 i__1 = (*i0 << 2) - 1 + *pp;
182 for (i4 = np; i4 >= i__1; i4 += -4) {
187 if (z__[i4] > z__[i4 - 2]) {
190 b2 *= z__[i4] / z__[i4 - 2];
192 if (dmax(b2,b1) * 100.f < a2 || .563f < a2) {
200 /* Rayleigh quotient residual bound. */
203 s = gam * (1.f - sqrt(a2)) / (a2 + 1.f);
206 } else if (*dmin__ == *dn2) {
213 /* Compute contribution to norm squared from I > NN-2. */
215 np = nn - (*pp << 1);
219 if (z__[np - 8] > b2 || z__[np - 4] > b1) {
222 a2 = z__[np - 8] / b2 * (z__[np - 4] / b1 + 1.f);
224 /* Approximate contribution to norm squared from I < NN-2. */
227 b2 = z__[nn - 13] / z__[nn - 15];
229 i__1 = (*i0 << 2) - 1 + *pp;
230 for (i4 = nn - 17; i4 >= i__1; i4 += -4) {
235 if (z__[i4] > z__[i4 - 2]) {
238 b2 *= z__[i4] / z__[i4 - 2];
240 if (dmax(b2,b1) * 100.f < a2 || .563f < a2) {
250 s = gam * (1.f - sqrt(a2)) / (a2 + 1.f);
254 /* Case 6, no information to guide us. */
257 g += (1.f - g) * .333f;
258 } else if (*ttype == -18) {
259 g = .083250000000000005f;
267 } else if (*n0in == *n0 + 1) {
269 /* One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN. */
271 if (*dmin1 == *dn1 && *dmin2 == *dn2) {
277 if (z__[nn - 5] > z__[nn - 7]) {
280 b1 = z__[nn - 5] / z__[nn - 7];
285 i__1 = (*i0 << 2) - 1 + *pp;
286 for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) {
288 if (z__[i4] > z__[i4 - 2]) {
291 b1 *= z__[i4] / z__[i4 - 2];
293 if (dmax(b1,a2) * 100.f < b2) {
299 b2 = sqrt(b2 * 1.05f);
300 /* Computing 2nd power */
302 a2 = *dmin1 / (r__1 * r__1 + 1.f);
303 gap2 = *dmin2 * .5f - a2;
304 if (gap2 > 0.f && gap2 > b2 * a2) {
306 r__1 = s, r__2 = a2 * (1.f - a2 * 1.01f * (b2 / gap2) * b2);
310 r__1 = s, r__2 = a2 * (1.f - b2 * 1.01f);
319 if (*dmin1 == *dn1) {
325 } else if (*n0in == *n0 + 2) {
327 /* Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN. */
329 /* Cases 10 and 11. */
331 if (*dmin2 == *dn2 && z__[nn - 5] * 2.f < z__[nn - 7]) {
334 if (z__[nn - 5] > z__[nn - 7]) {
337 b1 = z__[nn - 5] / z__[nn - 7];
342 i__1 = (*i0 << 2) - 1 + *pp;
343 for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) {
344 if (z__[i4] > z__[i4 - 2]) {
347 b1 *= z__[i4] / z__[i4 - 2];
349 if (b1 * 100.f < b2) {
355 b2 = sqrt(b2 * 1.05f);
356 /* Computing 2nd power */
358 a2 = *dmin2 / (r__1 * r__1 + 1.f);
359 gap2 = z__[nn - 7] + z__[nn - 9] - sqrt(z__[nn - 11]) * sqrt(z__[
361 if (gap2 > 0.f && gap2 > b2 * a2) {
363 r__1 = s, r__2 = a2 * (1.f - a2 * 1.01f * (b2 / gap2) * b2);
367 r__1 = s, r__2 = a2 * (1.f - b2 * 1.01f);
374 } else if (*n0in > *n0 + 2) {
376 /* Case 12, more than two eigenvalues deflated. No information. */